The evolution of $ft$ is governed by four parameters: $σΔa$, $μm$, $σm$, and $ρm$ (see equations [6] and [7]). Table 2a summarizes the posterior for these parameters. The posterior median for $σΔa$ is somewhat lower than a typical estimate for the United States, but this is consistent with using the OECD average for $ft$. The spread of the posterior is roughly what one would find using 16 i.i.d. normal observations, that is, using $q=16$ low-frequency observations with $Δft$ an i.i.d. process. The posterior for the average growth rate, $μm$, is centered around 1.9% per year with 67% error bands of roughly $±$1% per year. Figure 3b shows the posterior estimates for $mt$, the local level of $Δft$. The posterior median shows some variation over the sample, but a constant value of 1.9% (its mean) is within the (pointwise) 67% credible set for all dates.

Table 2.

Posterior Percentiles

a. Posterior percentiles for selected parameters, $ft$ and $ct$ processes
Percentiles of Posterior
Parameter0.050.170.500.840.95
i. Parameters for $ft$ process (in percentage points)
$σΔa$ 2.34 2.70 3.33 4.14 4.87
$μm$ −0.08 0.77 1.85 2.79 3.56
$σm$ 0.42 0.73 1.13 1.52 1.76
$hm$ 50 63 96 133 146
ii. Parameters for $c$ process
$μc$ −0.97 −0.83 −0.63 −0.45 −0.32
a. Posterior percentiles for selected parameters, $ft$ and $ct$ processes
Percentiles of Posterior
Parameter0.050.170.500.840.95
i. Parameters for $ft$ process (in percentage points)
$σΔa$ 2.34 2.70 3.33 4.14 4.87
$μm$ −0.08 0.77 1.85 2.79 3.56
$σm$ 0.42 0.73 1.13 1.52 1.76
$hm$ 50 63 96 133 146
ii. Parameters for $c$ process
$μc$ −0.97 −0.83 −0.63 −0.45 −0.32

$Δft=mt+Δat$, where $Δat$ is $I$(0) and $mt$ is a low-frequency AR(1) with mean $μm$ and low-frequency AR coefficient $ρm$. The half-life, $hm$, solves $ρmhm=1/2$.

b. Posterior percentiles for selected parameters, $ci,t$ process
Half-life$σc$$σ(ct+50-ct)$
Percentiles of Posterior
0.170.500.840.170.500.840.170.500.84
i. Pooled across countries
All countries 130 233 389 0.85 1.10 1.37 0.45 0.63 0.86
OECD 201 338 486 0.74 0.91 1.15 0.35 0.44 0.58
Non-OECD 121 211 342 0.91 1.15 1.40 0.52 0.68 0.89
ii. Selected countries
China 150 222 330 1.00 1.20 1.40 0.59 0.68 0.79
Singapore 111 185 291 0.92 1.13 1.34 0.61 0.72 0.86
Madagascar 148 214 317 1.08 1.24 1.42 0.61 0.72 0.85
Belgium 286 394 507 0.69 0.82 0.98 0.32 0.37 0.44
Russia 78 138 239 0.90 1.10 1.34 0.66 0.79 0.94
United States 303 413 529 0.75 0.89 1.06 0.34 0.39 0.45
Australia 340 461 567 0.71 0.84 1.00 0.30 0.34 0.40
Liberia 50 70 108 1.36 1.51 1.62 1.17 1.34 1.50
b. Posterior percentiles for selected parameters, $ci,t$ process
Half-life$σc$$σ(ct+50-ct)$
Percentiles of Posterior
0.170.500.840.170.500.840.170.500.84
i. Pooled across countries
All countries 130 233 389 0.85 1.10 1.37 0.45 0.63 0.86
OECD 201 338 486 0.74 0.91 1.15 0.35 0.44 0.58
Non-OECD 121 211 342 0.91 1.15 1.40 0.52 0.68 0.89
ii. Selected countries
China 150 222 330 1.00 1.20 1.40 0.59 0.68 0.79
Singapore 111 185 291 0.92 1.13 1.34 0.61 0.72 0.86
Madagascar 148 214 317 1.08 1.24 1.42 0.61 0.72 0.85
Belgium 286 394 507 0.69 0.82 0.98 0.32 0.37 0.44
Russia 78 138 239 0.90 1.10 1.34 0.66 0.79 0.94
United States 303 413 529 0.75 0.89 1.06 0.34 0.39 0.45
Australia 340 461 567 0.71 0.84 1.00 0.30 0.34 0.40
Liberia 50 70 108 1.36 1.51 1.62 1.17 1.34 1.50

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